Miro Heiskanen and Arttu Hyry each scored, and Casey DeSmith made 25 saves for the Stars (3-3-1). Dallas had lost two straight games (0-1-1), including a 3-2 loss to the Avalanche at home on Tuesday.
Jason Robertson also scored for Dallas in the shootout.
Gabriel Landeskog and Brock Nelson each also scored, Nazem Kadri had two assists and Scott Wedgewood made 20 saves for the Avalanche (4-2-1).
Kadri also scored in the shootout for Colorado.
After having two first period goals overturned, Landeskog put the Avalanche on the board 1-0 at 4:55 of the second period when he deflected Kadri’s initial shot while cutting across the crease. Kadri fired from the outside hash marks in the left circle and Landeskog was all alone in front to tip the shot past DeSmith.
Heiskanen tied it 1-1 at 15:03 with a wrist shot that went top shelf, short side over the right shoulder of Wedgewood from the left dot. Rantanen fed Heiskanen from outside the right circle for the play.
Hyry scored a short-handed goal at 1:20 of the third period to make it 2-1 Dallas. He intercepted a play from Cale Makar at his own blue line, outran the defenseman up the ice and to the net, and went forehand to backhand and past the glove of Wedgewood.
Nelson tied it 2-2 at 8:21 when he finished a bouncing puck short side around the right leg of DeSmith and into the open net. Artturi Lehkonen fired the initial shot, which caromed off Dallas defenseman Thomas Harley in front and over to Nelson on the left side for the wrister.
Avalanche forward Nicolas Roy didn’t play due to an upper-body injury. Makar, who missed Tuesday’s win for the birth of his twins, finished with plus-1 with two shots in 22:54 of ice time.
Stars forward Oskar Back left the game in the first period with an upper-body injury and didn’t return.